Problem: Simplify the following expression: $x = \dfrac{10n^2 + 60n - 70}{n + 7} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $10$ , so we can rewrite the expression: $ x =\dfrac{10(n^2 + 6n - 7)}{n + 7} $ Then we factor the remaining polynomial: $n^2 + {6}n {-7} $ ${7} {-1} = {6}$ ${7} \times {-1} = {-7}$ $ (n + {7}) (n {-1}) $ This gives us a factored expression: $\dfrac{10(n + {7}) (n {-1})}{n + 7}$ We can divide the numerator and denominator by $(n - 7)$ on condition that $n \neq -7$ Therefore $x = 10(n - 1); n \neq -7$